Spatial and behavioral types in the pi-calculus

We present a framework that combines ideas from spatial logics and behavioral type systems. Type systems for the pi-calculus are proposed where newly declared (restricted) names are annotated with spatial process properties, predicating on those names, that are expected to hold in the scope of the declaration. Types are akin to ccs terms and account for the process abstract behavior and ''shallow'' spatial structure. Type checking relies on spatial model checking, but properties are checked against types rather than against processes. Type soundness theorems ensure that, for a certain class of spatial properties, well-typed programs are also well annotated, in the sense that processes in the scope of any restriction do satisfy the corresponding annotation at run-time. The considered class of properties is rather general. Differently from previous proposals, it includes both safety and liveness ones, and is not limited to invariants. We also elaborate a distinction between locally and globally checkable properties.